When basophils with Immunoglobulin E (IgE) on their surface are incubated in vitro in the presence of calcium with an antigen that binds to the IgE, they release histamine. The antigen activates the basophil and triggers a series of events which culminates in degranulation. An essential step in the triggering is the crosslinking (bringing together) of two or more IgE molecules on the cell surface. Under certain experimental conditions incubation of basophils leads to cell desensitization rather than activation. In some cases the desensitizing incubation renders the cells unresponsive to any future IgE-mediated activation; in other cases the cells become unresponsive only to future challenges with the incubating antigen. Our long term goal is to quantitatively understand the activation and desensitization of basophils by allergens. In close collaboration with experiment, we propose to carry out theoretical studies on the interaction of sensitized basophils with a variety of crosslinking agents. Initially we will concentrate on synthetic bivalent haptens and synthetic dimers (two IgE molecules covalently linked), for they both offer unique ways to produce the basophil. These studies will serve as an introduction to our work on natural allergens.